Solve 5/9 * (7 - 6x) - 3/4 * (3 - 15x) * 1/12 * (3x - 5) - 1/2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{5}{9}(7-6x)-\frac{3}{4}(3-15x)\frac{1}{12}(3x-5)-\frac{1}{2}$$

Evaluate

$\frac{45x^{2}}{16}-\frac{103x}{12}+\frac{623}{144}$

Solution Steps

Use the distributive property to multiply $\frac{5}{9}$ by $7-6x$.

$$\frac{5}{9}\times 7+\frac{5}{9}\left(-6\right)x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\left(3x-5\right)-\frac{1}{2}$$

Express $\frac{5}{9}\times 7$ as a single fraction.

$$\frac{5\times 7}{9}+\frac{5}{9}\left(-6\right)x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\left(3x-5\right)-\frac{1}{2}$$

Multiply $5$ and $7$ to get $35$.

$$\frac{35}{9}+\frac{5}{9}\left(-6\right)x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\left(3x-5\right)-\frac{1}{2}$$

Express $\frac{5}{9}\left(-6\right)$ as a single fraction.

$$\frac{35}{9}+\frac{5\left(-6\right)}{9}x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\left(3x-5\right)-\frac{1}{2}$$

Multiply $5$ and $-6$ to get $-30$.

$$\frac{35}{9}+\frac{-30}{9}x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\left(3x-5\right)-\frac{1}{2}$$

Reduce the fraction $\frac{-30}{9}$ to lowest terms by extracting and canceling out $3$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\left(3x-5\right)-\frac{1}{2}$$

Multiply $\frac{3}{4}$ times $\frac{1}{12}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3\times 1}{4\times 12}\left(3-15x\right)\left(3x-5\right)-\frac{1}{2}$$

Do the multiplications in the fraction $\frac{3\times 1}{4\times 12}$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{48}\left(3-15x\right)\left(3x-5\right)-\frac{1}{2}$$

Reduce the fraction $\frac{3}{48}$ to lowest terms by extracting and canceling out $3$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{1}{16}\left(3-15x\right)\left(3x-5\right)-\frac{1}{2}$$

Use the distributive property to multiply $-\frac{1}{16}$ by $3-15x$.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{1}{16}\times 3-\frac{1}{16}\left(-15\right)x\right)\left(3x-5\right)-\frac{1}{2}$$

Express $-\frac{1}{16}\times 3$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x+\left(\frac{-3}{16}-\frac{1}{16}\left(-15\right)x\right)\left(3x-5\right)-\frac{1}{2}$$

Fraction $\frac{-3}{16}$ can be rewritten as $-\frac{3}{16}$ by extracting the negative sign.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{3}{16}-\frac{1}{16}\left(-15\right)x\right)\left(3x-5\right)-\frac{1}{2}$$

Express $-\frac{1}{16}\left(-15\right)$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{3}{16}+\frac{-\left(-15\right)}{16}x\right)\left(3x-5\right)-\frac{1}{2}$$

Multiply $-1$ and $-15$ to get $15$.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{3}{16}+\frac{15}{16}x\right)\left(3x-5\right)-\frac{1}{2}$$

Apply the distributive property by multiplying each term of $-\frac{3}{16}+\frac{15}{16}x$ by each term of $3x-5$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{16}\times 3x-\frac{3}{16}\left(-5\right)+\frac{15}{16}x\times 3x+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Multiply $x$ and $x$ to get $x^{2}$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{16}\times 3x-\frac{3}{16}\left(-5\right)+\frac{15}{16}x^{2}\times 3+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Express $-\frac{3}{16}\times 3$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x+\frac{-3\times 3}{16}x-\frac{3}{16}\left(-5\right)+\frac{15}{16}x^{2}\times 3+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Multiply $-3$ and $3$ to get $-9$.

$$\frac{35}{9}-\frac{10}{3}x+\frac{-9}{16}x-\frac{3}{16}\left(-5\right)+\frac{15}{16}x^{2}\times 3+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Fraction $\frac{-9}{16}$ can be rewritten as $-\frac{9}{16}$ by extracting the negative sign.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x-\frac{3}{16}\left(-5\right)+\frac{15}{16}x^{2}\times 3+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Express $-\frac{3}{16}\left(-5\right)$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{-3\left(-5\right)}{16}+\frac{15}{16}x^{2}\times 3+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Multiply $-3$ and $-5$ to get $15$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{15}{16}+\frac{15}{16}x^{2}\times 3+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Express $\frac{15}{16}\times 3$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{15}{16}+\frac{15\times 3}{16}x^{2}+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Multiply $15$ and $3$ to get $45$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{15}{16}+\frac{45}{16}x^{2}+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Express $\frac{15}{16}\left(-5\right)$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{15}{16}+\frac{45}{16}x^{2}+\frac{15\left(-5\right)}{16}x-\frac{1}{2}$$

Multiply $15$ and $-5$ to get $-75$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{15}{16}+\frac{45}{16}x^{2}+\frac{-75}{16}x-\frac{1}{2}$$

Fraction $\frac{-75}{16}$ can be rewritten as $-\frac{75}{16}$ by extracting the negative sign.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{15}{16}+\frac{45}{16}x^{2}-\frac{75}{16}x-\frac{1}{2}$$

Combine $-\frac{9}{16}x$ and $-\frac{75}{16}x$ to get $-\frac{21}{4}x$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{21}{4}x+\frac{15}{16}+\frac{45}{16}x^{2}-\frac{1}{2}$$

Combine $-\frac{10}{3}x$ and $-\frac{21}{4}x$ to get $-\frac{103}{12}x$.

$$\frac{35}{9}-\frac{103}{12}x+\frac{15}{16}+\frac{45}{16}x^{2}-\frac{1}{2}$$

Least common multiple of $9$ and $16$ is $144$. Convert $\frac{35}{9}$ and $\frac{15}{16}$ to fractions with denominator $144$.

$$\frac{560}{144}-\frac{103}{12}x+\frac{135}{144}+\frac{45}{16}x^{2}-\frac{1}{2}$$

Since $\frac{560}{144}$ and $\frac{135}{144}$ have the same denominator, add them by adding their numerators.

$$\frac{560+135}{144}-\frac{103}{12}x+\frac{45}{16}x^{2}-\frac{1}{2}$$

Add $560$ and $135$ to get $695$.

$$\frac{695}{144}-\frac{103}{12}x+\frac{45}{16}x^{2}-\frac{1}{2}$$

Least common multiple of $144$ and $2$ is $144$. Convert $\frac{695}{144}$ and $\frac{1}{2}$ to fractions with denominator $144$.

$$\frac{695}{144}-\frac{103}{12}x+\frac{45}{16}x^{2}-\frac{72}{144}$$

Since $\frac{695}{144}$ and $\frac{72}{144}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{695-72}{144}-\frac{103}{12}x+\frac{45}{16}x^{2}$$

Subtract $72$ from $695$ to get $623$.

$$\frac{623}{144}-\frac{103}{12}x+\frac{45}{16}x^{2}$$

Expand

$\frac{45x^{2}}{16}-\frac{103x}{12}+\frac{623}{144}$

Solution Steps

Use the distributive property to multiply $\frac{5}{9}$ by $7-6x$.

$$\frac{5}{9}\times 7+\frac{5}{9}\left(-6\right)x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\left(3x-5\right)-\frac{1}{2}$$

Express $\frac{5}{9}\times 7$ as a single fraction.

$$\frac{5\times 7}{9}+\frac{5}{9}\left(-6\right)x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\left(3x-5\right)-\frac{1}{2}$$

Multiply $5$ and $7$ to get $35$.

$$\frac{35}{9}+\frac{5}{9}\left(-6\right)x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\left(3x-5\right)-\frac{1}{2}$$

Express $\frac{5}{9}\left(-6\right)$ as a single fraction.

$$\frac{35}{9}+\frac{5\left(-6\right)}{9}x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\left(3x-5\right)-\frac{1}{2}$$

Multiply $5$ and $-6$ to get $-30$.

$$\frac{35}{9}+\frac{-30}{9}x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\left(3x-5\right)-\frac{1}{2}$$

Reduce the fraction $\frac{-30}{9}$ to lowest terms by extracting and canceling out $3$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\left(3x-5\right)-\frac{1}{2}$$

Multiply $\frac{3}{4}$ times $\frac{1}{12}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3\times 1}{4\times 12}\left(3-15x\right)\left(3x-5\right)-\frac{1}{2}$$

Do the multiplications in the fraction $\frac{3\times 1}{4\times 12}$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{48}\left(3-15x\right)\left(3x-5\right)-\frac{1}{2}$$

Reduce the fraction $\frac{3}{48}$ to lowest terms by extracting and canceling out $3$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{1}{16}\left(3-15x\right)\left(3x-5\right)-\frac{1}{2}$$

Use the distributive property to multiply $-\frac{1}{16}$ by $3-15x$.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{1}{16}\times 3-\frac{1}{16}\left(-15\right)x\right)\left(3x-5\right)-\frac{1}{2}$$

Express $-\frac{1}{16}\times 3$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x+\left(\frac{-3}{16}-\frac{1}{16}\left(-15\right)x\right)\left(3x-5\right)-\frac{1}{2}$$

Fraction $\frac{-3}{16}$ can be rewritten as $-\frac{3}{16}$ by extracting the negative sign.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{3}{16}-\frac{1}{16}\left(-15\right)x\right)\left(3x-5\right)-\frac{1}{2}$$

Express $-\frac{1}{16}\left(-15\right)$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{3}{16}+\frac{-\left(-15\right)}{16}x\right)\left(3x-5\right)-\frac{1}{2}$$

Multiply $-1$ and $-15$ to get $15$.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{3}{16}+\frac{15}{16}x\right)\left(3x-5\right)-\frac{1}{2}$$

Apply the distributive property by multiplying each term of $-\frac{3}{16}+\frac{15}{16}x$ by each term of $3x-5$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{16}\times 3x-\frac{3}{16}\left(-5\right)+\frac{15}{16}x\times 3x+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Multiply $x$ and $x$ to get $x^{2}$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{16}\times 3x-\frac{3}{16}\left(-5\right)+\frac{15}{16}x^{2}\times 3+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Express $-\frac{3}{16}\times 3$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x+\frac{-3\times 3}{16}x-\frac{3}{16}\left(-5\right)+\frac{15}{16}x^{2}\times 3+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Multiply $-3$ and $3$ to get $-9$.

$$\frac{35}{9}-\frac{10}{3}x+\frac{-9}{16}x-\frac{3}{16}\left(-5\right)+\frac{15}{16}x^{2}\times 3+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Fraction $\frac{-9}{16}$ can be rewritten as $-\frac{9}{16}$ by extracting the negative sign.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x-\frac{3}{16}\left(-5\right)+\frac{15}{16}x^{2}\times 3+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Express $-\frac{3}{16}\left(-5\right)$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{-3\left(-5\right)}{16}+\frac{15}{16}x^{2}\times 3+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Multiply $-3$ and $-5$ to get $15$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{15}{16}+\frac{15}{16}x^{2}\times 3+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Express $\frac{15}{16}\times 3$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{15}{16}+\frac{15\times 3}{16}x^{2}+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Multiply $15$ and $3$ to get $45$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{15}{16}+\frac{45}{16}x^{2}+\frac{15}{16}x\left(-5\right)-\frac{1}{2}$$

Express $\frac{15}{16}\left(-5\right)$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{15}{16}+\frac{45}{16}x^{2}+\frac{15\left(-5\right)}{16}x-\frac{1}{2}$$

Multiply $15$ and $-5$ to get $-75$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{15}{16}+\frac{45}{16}x^{2}+\frac{-75}{16}x-\frac{1}{2}$$

Fraction $\frac{-75}{16}$ can be rewritten as $-\frac{75}{16}$ by extracting the negative sign.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x+\frac{15}{16}+\frac{45}{16}x^{2}-\frac{75}{16}x-\frac{1}{2}$$

Combine $-\frac{9}{16}x$ and $-\frac{75}{16}x$ to get $-\frac{21}{4}x$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{21}{4}x+\frac{15}{16}+\frac{45}{16}x^{2}-\frac{1}{2}$$

Combine $-\frac{10}{3}x$ and $-\frac{21}{4}x$ to get $-\frac{103}{12}x$.

$$\frac{35}{9}-\frac{103}{12}x+\frac{15}{16}+\frac{45}{16}x^{2}-\frac{1}{2}$$

Least common multiple of $9$ and $16$ is $144$. Convert $\frac{35}{9}$ and $\frac{15}{16}$ to fractions with denominator $144$.

$$\frac{560}{144}-\frac{103}{12}x+\frac{135}{144}+\frac{45}{16}x^{2}-\frac{1}{2}$$

Since $\frac{560}{144}$ and $\frac{135}{144}$ have the same denominator, add them by adding their numerators.

$$\frac{560+135}{144}-\frac{103}{12}x+\frac{45}{16}x^{2}-\frac{1}{2}$$

Add $560$ and $135$ to get $695$.

$$\frac{695}{144}-\frac{103}{12}x+\frac{45}{16}x^{2}-\frac{1}{2}$$

Least common multiple of $144$ and $2$ is $144$. Convert $\frac{695}{144}$ and $\frac{1}{2}$ to fractions with denominator $144$.

$$\frac{695}{144}-\frac{103}{12}x+\frac{45}{16}x^{2}-\frac{72}{144}$$

Since $\frac{695}{144}$ and $\frac{72}{144}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{695-72}{144}-\frac{103}{12}x+\frac{45}{16}x^{2}$$

Subtract $72$ from $695$ to get $623$.

$$\frac{623}{144}-\frac{103}{12}x+\frac{45}{16}x^{2}$$